idk, I would never have played COD if it was multi-player only, and I can't be the only one. As said above the campaign can be "cinematic", in a way you're just not going to get in a deathmatch game.
Sure they could go multiplayer only and reduce the cost of development a little, but If single player and multiplayer are as distinct as people say, then they're effective creating two games for substationally less cost and risk of developing them separately, and they're able to leverage the same marketing budget to reach out to the two disctinct market segments at the same time. Otherwise people who would normally buy a single-player shooter are being exposed to the same advertising but they'd be going "meh, COD's
multiplayer only". Basically anyone who plays games primarily for the story wouldn't buy your multiplayer only game, because those are all grind and no narrative.
Going off data, it looks like about 1/3rd of all playstation owners finish the campaigns in COD. We could say "meh only 1/3rd", but that translates to
"50% more sales if you have a singleplayer option", which is of course an absolutely massive profit boost for a AAA game with a budget like COD. Only 1/3rd of players never touch the campaign at all, and the completion rate is almost identical to single-player only FPS's such as BioShock. That shows that single-player COD is alive and well. Probably, talking to the people who play online you get a massively biased sample of players.